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annotations.tex
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\chapter{Annotations}\label{annotations}
Annotations are intended for storing extra information about a model,
such as graphics, documentation or versioning, etc. A Modelica tool is
free to define and use other annotations, in addition to those defined
here, according to \cref{vendor-specific-annotations}. Annotations must be
represented with constructs according to the Modelica grammar (for
replaceable class declarations with a constraining-clause also refer to
\cref{constraining-clause-annotations}). The specification in this document defines the
semantic meaning if a tool implements any of these annotations.
\section{Vendor-Specific Annotations}\label{vendor-specific-annotations}
A vendor may -- anywhere inside an annotation -- add specific, possibly
undocumented, annotations which are not intended to be interpreted by
other tools. The only requirement is that any tool
shall save files with all vendor-specific annotations (and all annotations from this chapter) intact.
Two variants of vendor-specific annotations exist; one
simple and one hierarchical. Double underscore concatenated with a
vendor name as initial characters of the identifier are used to identify
vendor-specific annotations.
\begin{example}
\begin{lstlisting}[language=modelica]
annotation (
Icon(coordinateSystem(extent={{-100,-100}, {100,100}}),
graphics={__NameOfVendor(Circle(center={0,0}, radius=10))}) );
\end{lstlisting}
This introduces a new graphical primitive \lstinline!Circle! using the
hierarchical variant of vendor-specific annotations.
\begin{lstlisting}[language=modelica]
annotation (
Icon(coordinateSystem(extent={{-100,-100}, {100,100}}),
graphics={Rectangle(extent={{-5,-5},{7,7}}, __NameOfVendor_shadow=2)}) );
\end{lstlisting}
This introduces a new attribute \lstinline!__NameOfVendor_shadow!
for the \lstinline!Rectangle! primitive using the simple variant of
vendor-specific annotations.
\end{example}
\section{Annotations for Documentation}\label{annotations-for-documentation}
The \lstinline!Documentation! annotation has the following contents, where the \lstinline!info! and \lstinline!revisions! annotations are described in \cref{annotation-info-revisions}, and the \lstinline!figures! annotation is described in \cref{annotations-for-figures}:
\begin{lstlisting}[language=modelica]
record Documentation
String info = "" "Description of the class";
String revisions = "" "Revision history";
Figure[:] figures = {}; "Simulation result figures";
end Documentation;
\end{lstlisting}
How the tool interprets the information in \lstinline!Documentation! is unspecified.
\subsection{Class Description and Revision History}\label{annotation-info-revisions}
Inside the \lstinline!Documentation! annotation, the \lstinline!info! annotation gives a textual description of the class, and the \lstinline!revisions! annotation gives a revision history.
\begin{nonnormative}
The \lstinline!revisions! documentation may be omitted in printed documentation.
\end{nonnormative}
If the string starts with the tag \lstinline!<html>! or \lstinline!<HTML>! the entire string is HTML encoded (and is assumed to end with \lstinline!</html>! or \lstinline!</HTML>! and shall be rendered as HTML even if the end-tags are missing), otherwise the entire string is rendered as is. The HTML encoded content may contain links. For external links, see \cref{external-resources}. Links to Modelica classes may be defined with the HTML link command using scheme \lstinline!Modelica! (using its lower case form in the URI, see \cref{external-resources}), e.g.,
\begin{lstlisting}[language=modelica]
<a href="modelica://MultiBody.Tutorial">MultiBody.Tutorial</a>
\end{lstlisting}
Together with scheme \lstinline!Modelica! the (URI) fragment specifiers
\lstinline!#diagram!, \lstinline!#info!, \lstinline!#text!, \lstinline!#icon! may be used to reference different
layers. User-defined fragment specifiers (anchors) may also be used, and they may be renamed
when generating HTML (in particular to avoid collisions).
Example:
\begin{lstlisting}[language=modelica]
<a href="modelica://MultiBody.Joints.Revolute#info">Revolute</a>
\end{lstlisting}
\subsection{Annotations for Figures}\label{annotations-for-figures}
Inside the \lstinline!Documentation! annotation, each element of the \lstinline!figures! annotation array has the following content:
\begin{lstlisting}[language=modelica]
record Figure
String title = "" "Title meant for display";
String identifier "Identifier meant for programmatic access";
String group = "" "Name of plot group";
Boolean preferred = false "Automatically display figure after simulation";
Plot[:] plots "Plots";
String caption "Figure caption";
end Figure;
\end{lstlisting}
A \lstinline!Figure! is a graphical container that can contain several
\lstinline!plots! described by \lstinline!Plot! annotations:
\begin{lstlisting}[language=modelica]
record Plot
String title "Title meant for display";
String identifier "Identifier meant for programmatic access";
Curve[:] curves "Plot curves";
Axis x "X axis properties";
Axis y "Y axis properties";
end Plot;
\end{lstlisting}
A \lstinline!Plot! can contain several \lstinline!curves!, see \cref{plot-curves}, that all share a common \lstinline!x! and \lstinline!y! axis with properties described in \cref{axis-properties}.
Both \lstinline!Figure! and \lstinline!Plot! can have an optional title. When
the \lstinline!Figure! \lstinline!title! is the empty string (the default), the
tool must produce a non-empty title based on the figure content. On the other
hand, the \lstinline!Plot! \lstinline!title! has a tool-dependent default, but
the default may be the empty string. When the \lstinline!Plot! \lstinline!title! is the empty string, no
title should be shown. The plot title is not to be confused with the plot
\emph{label} which is never empty, see below. Variable replacements, as
described in \cref{variable-replacements}, can be used in the
\lstinline!title! of \lstinline!Figure! and \lstinline!Plot!.
The \lstinline!identifier! in \lstinline!Figure! and \lstinline!Plot! is an optional \lstinline!String! identifier, and is intended to identify the
\lstinline!Figure! and \lstinline!Plot! for programmatic access. The \lstinline!figures! annotation is inherited in the sense that each class has
a collection of figures comprised by the contents of the \lstinline!figures! annotation in the class itself, as well as the \lstinline!figures! annotations
from any base classes. A \lstinline!Figure! must be uniquely identified by its \lstinline!identifier! and a class having it in its collection. This
means that a \lstinline!Figure! \lstinline!identifier! must be unique among all \lstinline!Figure! annotations within the same \lstinline!figures!
annotation as well as among all \lstinline!figures! annotations from inherited classes. A \lstinline!Plot! \lstinline!identifier! on the other hand
is only required to be unique among the \lstinline!plots! in the the same \lstinline!Figure! annotation.
\begin{nonnormative}
For \lstinline!Figure!, this makes it possible to reference the plot from a
tool-specific scripting environment. For \lstinline!Plot!, this makes it
possible to reference the plot in the figure caption, which becomes useful when
the \lstinline!Figure! contains more than one \lstinline!Plot!.
\end{nonnormative}
% henrikt-ma 2020-06: Once there is Modelica URI support for referring to a figure in the collection of a class, it will be easier to explain
% the following statement...
Even though a \lstinline!Figure! annotation can be shared through inheritance between classes in a class hierarchy, note that each simulated class provides
its own data to be displayed in the figure.
Every \lstinline!Plot! has an automatically generated \emph{label} which is
required to be shown as soon as at least one \lstinline!Plot! in the
\lstinline!Figure! has an \lstinline!identifier!. A tool is free to choose both
labeling scheme (such as \emph{a}, \emph{b}, \dots, or \emph{i}, \emph{ii}, \dots), placement in the plot,
and styling in the plot itself as well as in other contexts.
When a \lstinline!Figure! defines a non-empty \lstinline!group!, it is used to
organize figures similar to how \lstinline!group! is used in the
\lstinline!Dialog! annotation (see \cref{annotations-for-the-graphical-user-interface}). However, leaving \lstinline!group! at
the default of an empty string does not mean that a group will be created
automatically, but that the figure resides outside of any group. The
\lstinline!group! is both the key used for grouping, and the name of the group
for display purposes.
The \lstinline!preferred! attribute of \lstinline!Figure! indicates whether the figure should be given preference when automatically determining which figures to show,
and a class may define any number of \lstinline!preferred! figures. For example, a tool might choose to automatically show all preferred figures when the class is simulated.
The \lstinline!caption! attribute of \lstinline!Figure! can use the restricted
form of text markup described in \cref{text-markup-in-captions} as well as
the variable replacements described in \cref{variable-replacements}.
\subsubsection{Axis Properties}\label{axis-properties}
Properties may be defined for each \lstinline!Plot! axis:
\begin{lstlisting}[language=modelica]
record Axis
Real min "Axis lower bound, in 'unit'";
Real max "Axis upper bound, in 'unit'";
String unit = "" "Unit of axis tick labels";
String label "Axis label";
end Axis;
\end{lstlisting}
When an axis bound isn't provided, the tool computes one automatically.
An empty \lstinline!unit! means that the axis is unitless, and each expression plotted against it may use its own unit determined by the tool. The tool is responsible for conveying the information
about choice of unit for the different variables, for instance by attaching this information to curve legends.
The Modelica tool is responsible for showing that values at the axis tick marks are expressed in \lstinline!unit!, so the axis \lstinline!label! shall not contain this information.
\begin{nonnormative}
When \lstinline!unit! is empty, and axis bounds are to be determined automatically, a natural choice of unit could be the variable's \lstinline!displayUnit!. When axis bounds are specified by the
user, on the other hand, a tool may choose a unit for the variable such that the range of the variable values (expressed in the chosen unit) fit nicely with the range of the unitless axis.
\end{nonnormative}
If a tool does not recognize the \lstinline!unit!, it is recommended to issue a warning and treat the \lstinline!unit! as if it was empty, as well as ignore any setting for \lstinline!min! and \lstinline!max!.
When an axis label isn't provided, the tool produces a default label. Providing the empty string as axis label means that no label should be shown. Variable replacements, as described in
\cref{variable-replacements}, can be used in the \lstinline!label! of \lstinline!Axis! The Modelica tool is responsible for showing the unit used for values at the axis tick marks, so the axis
\lstinline!label! shall not contain the unit.
\subsubsection{Plot Curves}\label{plot-curves}
The actual data to plot is specified in the \lstinline!curves! of a \lstinline!Plot!:
\begin{lstlisting}[language=modelica]
record Curve
expression x = time "X coordinate values";
expression y "Y coordinate values";
String legend "Legend";
end Curve;
\end{lstlisting}
The mandatory \lstinline!x! and \lstinline!y! expressions are restricted to be
component references refering to a scalar variable or \lstinline!time!. It
is an error if \lstinline!x! or \lstinline!y! does not designate a scalar variable.
When the \lstinline!unit! of an \lstinline!Axis! is non-empty, it is an error if the unit of the corresponding \lstinline!Curve! expression (i.e., a variable's \lstinline!unit!,
or second for \lstinline!time!) is incompatible with the axis unit.
When \lstinline!legend! isn't provided, the tool produces a default based on
\lstinline!x! and/or \lstinline!y!. Providing the empty string as
\lstinline!legend! means that the curve shall be omitted from the plot legend.
Variable replacements, as described in \cref{variable-replacements}, can be
used in the \lstinline!legend! of \lstinline!Curve!
\subsubsection{Escape sequences}\label{text-markup-escape-sequences}
In an attribute inside a figure where the variable replacements of \cref{variable-replacements} or the text markup of \cref{text-markup-in-captions} can be used, the following use of \firstuse{text markup escape sequences} applies. These escape sequences are applied after the application of other markup, and is not applied at all inside some of the other markup, see details for the respective markup.
The percent character `\%' shall be encoded \lstinline!%%!. The following are all the recognized escape sequences:
\begin{center}
\begin{tabular}{c c l}
\hline
\tablehead{Sequence} & \tablehead{Encoded character} & \tablehead{Comment}\\
\hline
\hline
\lstinline!%%! & `\%' & Only way to encode character. \\
\lstinline!%]! & `]' & Escape sequence only needed in link text. \\
\hline
\end{tabular}
\end{center}
\begin{nonnormative}
With the percent character being encoded as \lstinline!%%!, the behavior of \lstinline!%! appearing in any other way than the escape sequences above, for variable replacement (\cref{variable-replacements}), or for link markup (\cref{text-markup-in-captions}) is undefined, and thus possible to define in the future without breaking backward compatibility.
\end{nonnormative}
\subsubsection{Variable Replacements}\label{variable-replacements}
In the places listed in \cref{attributes-with-variable-replacements} where text for display is defined, the final value of a result variable can be embedded by refering to the variable as \lstinline!%{inertia1.w}!. This is similar to the \lstinline!Text! graphical primitive in \cref{text}.
\begin{table}[H]
\caption{Attributes that can use variable replacements.}
\label{attributes-with-variable-replacements}
\begin{center}
\begin{tabular}{l l}
\hline
\tablehead{Attribute} & \tablehead{Annotation}\\
\hline
\hline
\lstinline!title! & \lstinline!Figure! and \lstinline!Plot! \\
\lstinline!caption! & \lstinline!Figure! \\
\lstinline!legend! & \lstinline!Curve! \\
\lstinline!label! & \lstinline!Axis! \\
\hline
\end{tabular}
\end{center}
\end{table}
In \lstinline!%{$\mathit{variable}$}!, text markup escape sequences don't apply inside the $\mathit{variable}$, which has the form of \lstinline[language=grammar]!component-reference! in the grammar (\cref{expressions1}). This means that a complete \lstinline[language=grammar]!component-reference! shall be scanned before looking for the terminating closing brace.
\begin{example}
The variable replacement \lstinline!%{'%%'}! references the variable \lstinline!'%%'!, not the variable \lstinline!'%'!.
\end{example}
\begin{example}
The variable replacement \lstinline!%{foo . '}bar{'}! makes a valid reference to the variable\linebreak[4] \lstinline!foo.'}bar{'!.
\end{example}
Note that expansion to the final value means that expansion is not restricted to
parameters and constants, so that values to be shown in a caption can be
determined during simulation.
\begin{nonnormative}
By design, neither \lstinline!%class! nor \lstinline!%name! is supported in this context, as this information is expected to already be easily accessible (when applicable) in tool-specific ways. (Titles making use of \lstinline!%class! or \lstinline!%name! would then only lead to ugly duplication of this information.)
\end{nonnormative}
\subsubsection{Text Markup in Captions}\label{text-markup-in-captions}
In addition to variable replacements, a very restricted form of text markup is used for the \lstinline!caption!. Note that the text markup escape sequences described in \cref{text-markup-escape-sequences} generally apply inside \lstinline!caption!, with one exception given below for links.
Links take the form \lstinline!%[$\mathit{text}$]($\mathit{link}$)!, where the \lstinline![$\mathit{text}$]! part is optional except for vendor-specific links, and text markup escape sequences don't apply inside the $\mathit{link}$. The $\mathit{link}$ can be in either of the following forms, where the interpretation is given by the first matching form:
\begin{itemize}
\item A \lstinline!variable:$\mathit{id}$!, where $\mathit{id}$ is a component reference in the form of \lstinline[language=grammar]!component-reference! in the grammar, such as \lstinline!inertia1.w!.
% The 'plot:id' form below should be deprecated in favor of using an improved form of Modelica URI reference in the future, making 'variable:id' the only non-URI reference.
\item A \lstinline!plot:$\mathit{id}$!, where $\mathit{id}$ is the identifier of a \lstinline!Plot! in the current \lstinline!Figure!.
\item A vendor-specific URI expressed using a URI with scheme \lstinline!__$\mathit{nameOfVendor}$!, where $\mathit{nameOfVendor}$ is in the form of a valid URI scheme, conveying the name of the vendor defining the meaning of the link. A tool which does not understand the vendor-specific meaning of the link shall not send the URI to the operating system for interpretation, but only display the $\mathit{text}$ (which is mandatory for this form of link). A tool which understands the vendor-specific meaning is not required to use the $\mathit{text}$. A link with vendor-specific URI is denoted a \firstuse{vendor-specific link}.
% Use very short Modelica URI combined with carefull chosen wording below to deal with difficult line breaking.
\item A normal URI. Well established schemes such as \lstinline[language={[nocomment]modelica}]!https://github.com/modelica! or \lstinline[language={[nocomment]modelica}]!modelica://Modelica!, as well as lesser known schemes may be used. (A tool that has no special recognition of a scheme can try sending the URI to the operating system for interpretation.)
\end{itemize}
When \lstinline![$\mathit{text}$]! is omitted, a Modelica tool is free to derive a default based on the $\mathit{link}$.
\begin{example}
One application of a vendor-specific link is to prototype a feature that can later be turned into standardized markup. For example, say that the tool AVendor wants to generalize the variable replacements such that the duration of a simulation can be substituted into a caption. During the development, this could be represented as the vendor-specific link \lstinline!%[10 s](__AVendor:?duration)!, if the simulation has a duration of 10~seconds at the time of writing the caption. When AVendor renders this ``link'', it ignores the link text \lstinline!10 s! and just displays the actual duration instead, not linked to anything. Later, if this would become supported by standard markup, it might take the form of something like \lstinline!%{experiment:duration}! instead (note that \lstinline!experiment:duration! is not in the form of a component reference, avoiding conflict with current use of variable replacements).
\end{example}
\begin{nonnormative}
Note that for the character `]' to appear in $\mathit{text}$, it needs to be encoded as the escape sequence \lstinline!%]!, or it would be interpreted as the terminating delimiter of the \lstinline![$\mathit{text}$]!.
Similarly, the closing parenthesis `)' must be handled with care in $\mathit{link}$ in order to not be interpreted as the terminating delimiter of the \lstinline!($\mathit{link}$)!.
\begin{itemize}
\item For a \lstinline!variable:!, no special treatment is needed, as the component reference syntax of the \lstinline!<id>! allows parentheses to appear without risk of misinterpretation inside a quoted identifier. For example, \lstinline"%(variable:'try)me!')" has a parenthesis in \lstinline"'try)me!'" that must not be mistaken for the end of the \lstinline!($\mathit{link}$)!.
% The following shortcoming would be resolved if the 'plot:id' form was replaced by a Modelica URI reference, thanks to URL encoding.
\item For a \lstinline!plot:!, there is currently no way to reference a plot with `)' in its \lstinline!identifier!.
\item For a URI, a closing parenthesis must be URL encoded in order to not be interpreted as the end of the \lstinline!($\mathit{link}$)!. For example, the URL in \lstinline[language={[nocomment]modelica}]!%(http://bad.org/(tryme))! is just \filename{http://bad.org/(tryme}, and the entire link is followed by a stray closing parenthesis. To make it work, one has to use URL encoding: \lstinline[language={[nocomment]modelica}]!%(http://bad.org/%28tryme%29)! (using URL encoding of the opening parenthesis just for symmetry, and note that the \lstinline!%! of the percent-encoded sequences are not subject to text markup escape sequences).
\end{itemize}
\end{nonnormative}
The styling of the link text, as well as the link action, is left for each Modelica
tool to decide.
\begin{nonnormative}
For example, \lstinline!%(inertia1.w)! could be displayed as the text
\lstinline!inertia1.w! formatted with upright monospaced font, and have a pop-up
menu attached with menu items for plotting the variable, setting its start
value, or investigating the equation system from which it is solved. On the
other hand, \lstinline!%[angular velocity](inertia1.w)! could be formatted in
the same style as the surrounding text, except some non-intrusive visual clue
about it being linked.
\end{nonnormative}
\begin{nonnormative}
% This non-normative text explains why we don't want to assume that the 'link' must have a scheme, which has to be considered in the design of the vendor-specific link format.
Note that $\mathit{link}$ is currently not allowed to be a \emph{URI reference}, i.e., a URI or a \emph{relative reference} such as \lstinline!#foo!. This is due to to the current inability to define a base URI referencing the current figure. Once this becomes possible, the URI form of $\mathit{link}$ may be changed into a URI reference.
\end{nonnormative}
A sequence of one or more newlines (encoded either literally or using the \lstinline!\n!
escape sequence) means a paragraph break. (A line break within a paragraph is
not supported, and any paragraph break before the first paragraph or after the last
paragraph has no impact.)
\section{Annotations for Code Generation}\label{annotations-for-code-generation}
The annotations listed below, appearing directly inside \lstinline!annotation($\ldots$)!, can influence the code generation.
\begin{center}
\begin{tabular}{l|l l}
\hline
\tablehead{Annotation} & \tablehead{Description} & \tablehead{Details}\\
\hline
\hline
\lstinline!Evaluate! & Use parameter value for symbolic processing & \Cref{modelica:Evaluate}\\
\lstinline!HideResult! & Don't show component's simulator result & \Cref{modelica:HideResult}\\
\lstinline!Inline! & Inline function & \Cref{modelica:Inline}\\
\lstinline!LateInline! & Inline after all symbolic transformations & \Cref{modelica:LateInline}\\
\lstinline!InlineAfterIndexReduction! & Inline after index reduction & \Cref{modelica:InlineAfterIndexReduction}\\
\lstinline!GenerateEvents! & Generate events for zero crossings in function & \Cref{modelica:GenerateEvents}\\
\lstinline!smoothOrder! & Function smoothness guarantee & \Cref{modelica:smoothOrder}\\
\hline
\end{tabular}
\end{center}
\begin{annotationdefinition}[Evaluate]
\begin{synopsis}[grammar]\begin{lstlisting}
"Evaluate" "=" ( false | true )
\end{lstlisting}\end{synopsis}
\begin{semantics}
The annotation \lstinline!Evaluate! can occur in the component declaration, its type declaration, or a base-class of the type-declaration. In the case of multiple conflicting annotations it is handled similarly to modifiers (e.g., an \lstinline!Evaluate! annotation on the component declaration takes precedence). The annotation \lstinline!Evaluate! only has effect for a component declared with the prefix \lstinline!parameter!.
If \lstinline!Evaluate = true!, the model developer proposes to utilize the value for the symbolic processing. In that case, it is not possible to change the parameter value after symbolic pre-processing.
If \lstinline!Evaluate = false!, the model developer proposes to not utilize the value of the corresponding parameter for the symbolic processing.
\begin{nonnormative}
\lstinline!Evaluate! is for example used for axis of rotation parameters in the \lstinline!Modelica.Mechanics.MultiBody! library in order to improve the efficiency of the generated code.
\end{nonnormative}
\end{semantics}
\end{annotationdefinition}
\begin{annotationdefinition}[HideResult]
\begin{synopsis}[grammar]\begin{lstlisting}
"HideResult" "=" ( false | true )
\end{lstlisting}\end{synopsis}
\begin{semantics}
\lstinline!HideResult = true! defines that the model developer proposes to not show the simulator results of the corresponding component.
\lstinline!HideResult = false! defines that the developer proposes to show the corresponding component.
\begin{nonnormative}
For example, a tool is not expected to provide means to plot a variable with \lstinline!HideResult = true!. If a variable is declared in a protected section, a tool might not include it in a simulation result. By setting \lstinline!HideResult = false!, the modeler would like to have the variable in the simulation result, even if in the protected section.
\lstinline!HideResult! is for example used in the connectors of the \lstinline!Modelica.StateGraph! library to not show variables to the modeler that are of no interest to him and would confuse him.
\end{nonnormative}
\end{semantics}
\end{annotationdefinition}
\begin{annotationdefinition}[Inline]
\begin{synopsis}[grammar]\begin{lstlisting}
"Inline" "=" ( false | true )
\end{lstlisting}\end{synopsis}
\begin{semantics}
Has only an effect within a function declaration.
If \lstinline!Inline = true!, the model developer proposes to inline the function. This means, that the body of the function is included at all places where the function is called.
If \lstinline!Inline = true!, the model developer proposes to not inline the function.
\begin{nonnormative}
\lstinline!Inline = true! is for example used in \lstinline!Modelica.Mechanics.MultiBody.Frames! and in functions of \lstinline!Modelica.Media! to have no overhead for function calls such as resolving a vector in a different coordinate system and at the same time the function can be analytically differentiated, e.g., for index reduction needed for mechanical systems.
\end{nonnormative}
\end{semantics}
\end{annotationdefinition}
\begin{annotationdefinition}[LateInline]
\begin{synopsis}[grammar]\begin{lstlisting}
"LateInline" "=" ( false | true )
\end{lstlisting}\end{synopsis}
\begin{semantics}
Has only an effect within a function declaration.
If \lstinline!LateInline = true!, the model developer proposes to inline the function after all symbolic transformations have been performed.
\begin{nonnormative}
Late inlining is especially useful for differentiation and inversion of functions; for efficiency reasons it is then useful to replace all function calls with identical input arguments by one function call, before the inlining.
\end{nonnormative}
If \lstinline!LateInline = false!, the model developer proposes to not inline the function after symbolic transformations have been performed.
\lstinline!Inline = true, LateInline = false! is identical to \lstinline!Inline = true!.
\lstinline!Inline = true, LateInline = true! is identical to \lstinline!LateInline = true!.
\lstinline!Inline = false, LateInline = true! is identical to \lstinline!LateInline = true!.
\begin{nonnormative}
This annotation is for example used in \lstinline!Modelica.Media.Water.IF97_Utilities.T_props_ph! to provide in combination with common subexpression elimination the automatic caching of function calls. Furthermore, it is used in order that a tool is able to propagate specific enthalpy over connectors in the \lstinline!Modelica.Fluid! library.
\end{nonnormative}
\end{semantics}
\end{annotationdefinition}
\begin{annotationdefinition}[InlineAfterIndexReduction]
\begin{synopsis}[grammar]\begin{lstlisting}
"InlineAfterIndexReduction" "=" ( false | true )
\end{lstlisting}\end{synopsis}
\begin{semantics}
Has only an effect within a function declaration.
If \lstinline!true!, the model developer proposes to inline the function after the function is differentiated for index reduction, and before any other symbolic transformations are performed. This annotation cannot be combined with annotations \lstinline!Inline! and \lstinline!LateInline!.
\end{semantics}
\end{annotationdefinition}
\begin{annotationdefinition}[GenerateEvents]
\begin{synopsis}[grammar]\begin{lstlisting}
"GenerateEvents" "=" ( false | true )
\end{lstlisting}\end{synopsis}
\begin{semantics}
Has only an effect within a function declaration
If \lstinline!GenerateEvents = true!, the model developer proposes that crossing functions in the function should generate events (one possibility of doing this is to inline the function and generate events for the inlined function).
\begin{nonnormative}
This annotation is for example used in \lstinline!Modelica.Media.Water.IF97_Utilities.phase_dT! to indicate that the output should generate an event when it changes.
\end{nonnormative}
\end{semantics}
\end{annotationdefinition}
\begin{annotationdefinition}[smoothOrder]
\begin{synopsis}[grammar]\begin{lstlisting}
"smoothOrder" "=" UNSIGNED-NUMBER ")"
"smoothOrder" "(" "normallyConstant" "=" IDENT
{ "," "normallyConstant" "=" IDENT } ")" "=" UNSIGNED-NUMBER ")"
\end{lstlisting}\end{synopsis}
\begin{semantics}
This annotation has only an effect within a function declaration.
\lstinline!smoothOrder! defines the number of differentiations of the function, in order that all of the differentiated outputs are continuous provided all input arguments and their derivatives up to order \lstinline!smoothOrder! are continuous.
\begin{nonnormative}
This means that the function is at least C\textsuperscript{smoothOrder}. \lstinline!smoothOrder = 1! means that the function can be differentiated at least once in order that all output arguments are still continuous, provided the input arguments are continuous. If a tool needs the derivative of a function, e.g.\ for index reduction or to compute an analytic Jacobian, the function can be differentiated analytically at least \lstinline!smoothOrder! times.
\end{nonnormative}
The optional argument \lstinline!normallyConstant! of \lstinline!smoothOrder! defines that the function argument \lstinline!IDENT! is usually constant.
\begin{nonnormative}
A tool might check whether the actual argument to \lstinline!IDENT! is a parameter expression at the place where the function is called. If this is the case, the derivative of the function might be constructed under the assumption that the corresponding argument is constant, to enhance efficiency. Typically, a tool would generate at most two different derivative functions of a function: One, under the assumption that all \lstinline!normallyConstant! arguments are actually constant. And one, under the assumption that all input arguments are time varying. Based on the actual arguments of the function call either of the two derivative functions is used.
This annotation is used by many functions of the \lstinline!Modelica.Fluid! library, such as\linebreak[4] \lstinline!Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_laminar_DP!, since geometric arguments to these functions are usually constant.
\end{nonnormative}
\end{semantics}
\end{annotationdefinition}
\section{Annotations for Simulation Experiments}\label{annotations-for-simulation-experiments}
\begin{lstlisting}[language=grammar]
experiment-annotation:
annotation "(" "experiment" [ "(" [experimentOption
{"," experimentOption}] ")" ] ")"
experimentOption:
"StartTime" "=" [ "+" | "-" ] UNSIGNED-NUMBER |
"StopTime" "=" [ "+" | "-"] UNSIGNED-NUMBER |
"Interval" "=" UNSIGNED-NUMBER |
"Tolerance" "=" UNSIGNED-NUMBER
\end{lstlisting}
The experiment annotation defines the default start time (StartTime) in
{[}s{]}, the default stop time (StopTime) in {[}s{]}, the suitable time
resolution for the result grid (Interval) in {[}s{]}, and the default
relative integration tolerance (Tolerance) for simulation experiments to
be carried out with the model or block at hand. If StartTime is not specified it is assumed to be \lstinline!0.0!.
\section{Annotation for single use of class}\label{annotation-for-single-use-of-class}
For state machines it is useful to have single instances of local
classes. This can be done using:
\begin{lstlisting}[language=modelica]
annotation(singleInstance=true)
\end{lstlisting}
The annotation singleInstance in a class indicates that there should
only be one component instance of the class, and it should be in the
same scope as the class is defined. The intent is to remove the class
when the component is removed and to prevent duplication of the
component.
\section{Annotations for Graphical Objects}\label{annotations-for-graphical-objects}
A graphical representation of a class consists of two abstraction
layers, icon layer and diagram layer showing graphical objects,
component icons, connectors and connection lines. The icon
representation typically visualizes the component by hiding hierarchical
details. The hierarchical decomposition is described in the diagram
layer showing icons of subcomponents and connections between these.
Graphical annotations described in this chapter ties into the Modelica
grammar as follows.
\begin{lstlisting}[language=grammar]
graphical-annotations :
annotation "(" [ layer-annotations ] ")"
layer-annotations :
( icon\_layer | diagram\_layer ) [ "," layer-annotations ]
\end{lstlisting}
Layer descriptions (start of syntactic description):
\begin{lstlisting}[language=grammar]
icon-layer :
"Icon" "(" [ coordsys-specification "," ] graphics ")"
diagram-layer :
"Diagram" "(" [ coordsys-specification "," ] graphics ")"
\end{lstlisting}
\begin{example}
\begin{lstlisting}[language=modelica]
annotation (
Icon(coordinateSystem(extent={{-100,-100}, {100,100}}),
graphics={Rectangle(extent={{-100,-100}, {100,100}}),
Text(extent={{-100,-100}, {100,100}}, textString="Icon")}));
\end{lstlisting}
\end{example}
The graphics is specified as an ordered sequence of graphical
primitives, which are described below. First base-class contents is
drawn according to the order of the extends-clauses, and then graphical
primitives are drawn according to the order such that later objects can
cover earlier ones.
\begin{nonnormative}
Note that the ordered sequence is syntactically a valid Modelica annotation, although there
is no mechanism for defining an array of heterogeneous objects in Modelica.
\end{nonnormative}
These Icon, Diagram, and Documentation annotations are only allowed
directly in classes (e.g.\ not on components or connections). The allowed
annotations for a short class definition is the union of the allowed
annotations in classes and on extends-clauses.
\subsection{Common Definitions}\label{common-definitions}
The following common definitions are used to define graphical
annotations in the later sections.
\begin{lstlisting}[language=modelica]
type DrawingUnit = Real(final unit="mm");
type Point = DrawingUnit[2] "{x, y}";
type Extent = Point[2] "Defines a rectangular area {{x1, y1}, {x2, y2}}";
\end{lstlisting}
The interpretation of \lstinline!unit! is with respect to printer output in
natural size (not zoomed).
All graphical entities have a visible attribute which indicates if the
entity should be shown.
\begin{lstlisting}[language=modelica]
partial record GraphicItem
Boolean visible = true;
Point origin = {0, 0};
Real rotation(quantity="angle", unit="deg")=0;
end GraphicItem;
\end{lstlisting}
The \lstinline!origin! attribute specifies the origin of the graphical item in the
coordinate system of the layer in which it is defined. The origin is
used to define the geometric information of the item and for all
transformations applied to the item. All geometric information is given
relative the \lstinline!origin! attribute, which by default is \{0, 0\}.
The \lstinline!rotation! attribute specifies the rotation of the graphical item
counter-clockwise around the point defined by the \lstinline!origin! attribute.
\subsubsection{Coordinate Systems}\label{coordinate-systems}
Each of the layers has its own coordinate system. A coordinate system is
defined by the coordinates of two points, the left (x1) lower (y1)
corner and the right (x2) upper (y2) corner, where the coordinates of
the first point shall be less than the coordinates of the second point.
The attribute \lstinline!preserveAspectRatio! specifies a hint for the shape of
components of the class, but does not actually influence the rendering of the component.
If \lstinline!preserveAspectRatio! is true, changing the
extent of components should preserve the current aspect ratio of the coordinate
system of the class.
The attribute \lstinline!initialScale! specifies the default component size as
\lstinline!initialScale! times the size of the coordinate system of the class. An
application may use a different default value of \lstinline!initialScale!.
The attribute \lstinline!grid! specifies the spacing between grid points which can
be used by tools for alignment of points in the coordinate system, e.g.\ ``snap-to-grid''.
Its use and default value is tool-dependent.
\begin{lstlisting}[language=modelica]
record CoordinateSystem
Extent extent;
Boolean preserveAspectRatio=true;
Real initialScale = 0.1;
DrawingUnit grid[2];
end CoordinateSystem;
\end{lstlisting}
\begin{example}
A coordinate system for an icon could for example be defined as:
\begin{lstlisting}[language=modelica]
CoordinateSystem(extent = {{-10, -10}, {10, 10}});
\end{lstlisting}
i.e.\ a coordinate system with width 20 units and height 20 units.
\end{example}
The coordinate systems for the icon and diagram layers are by default
defined as follows; where the array of \lstinline!GraphicsItem! represents an
ordered list of graphical primitives.
\begin{lstlisting}[language=modelica]
record Icon "Representation of the icon layer"
CoordinateSystem coordinateSystem(extent = {{-100, -100}, {100, 100}});
GraphicItem[:] graphics;
end Icon;
record Diagram "Representation of the diagram layer"
CoordinateSystem coordinateSystem(extent = {{-100, -100}, {100, 100}});
GraphicItem[:] graphics;
end Diagram;
\end{lstlisting}
The coordinate system (including preserveAspectRatio) of a class is
defined by the following priority:
\begin{enumerate}
\item
The coordinate system annotation given in the class (if specified).
\item
The coordinate systems of the first base-class where the extent on the
extends-clause specifies a null-region (if any). Note that null-region
is the default for base-classes, see \cref{extends-clause}.
\item
The default coordinate system CoordinateSystem(extent=\{\{-100,
-100\}, \{100, 100\}\}).
\end{enumerate}
\subsubsection{Graphical Properties}\label{graphical-properties}
Properties of graphical objects and connection lines are described using
the following attribute types.
\begin{lstlisting}[language=modelica]
type Color = Integer[3](min=0, max=255) "RGB representation";
constant Color Black = zeros(3);
type LinePattern = enumeration(None, Solid, Dash, Dot, DashDot, DashDotDot);
type FillPattern = enumeration(None, Solid, Horizontal, Vertical,
Cross, Forward, Backward, CrossDiag, HorizontalCylinder, VerticalCylinder, Sphere);
type BorderPattern = enumeration(None, Raised, Sunken, Engraved);
type Smooth = enumeration(None, Bezier);
type EllipseClosure = enumeration(None, Chord, Radial);
\end{lstlisting}
The \lstinline!LinePattern! attribute \lstinline!Solid! indicates a normal line, \lstinline!None! an
invisible line, and the other attributes various forms of dashed/dotted
lines.
The \lstinline!FillPattern! attributes \lstinline!Horizontal!, \lstinline!Vertical!,
\lstinline!Cross!, \lstinline!Forward!,
\lstinline!Backward! and \lstinline!CrossDiag! specify fill patterns drawn with the line color
over the fill color.
The attributes \lstinline!HorizontalCylinder!, \lstinline!VerticalCylinder! and \lstinline!Sphere! specify
gradients that represent a horizontal cylinder, a vertical cylinder and
a sphere, respectively. The gradient goes from line color to fill color.
The border pattern attributes \lstinline!Raised!, \lstinline!Sunken! and \lstinline!Engraved! represent frames which are rendered in a tool-dependent way --- inside the extent of the filled shape.
\begin{figure}[H]
\begin{center}
\includegraphics{bezierpoints}
\end{center}
\caption{Line with \lstinline!smooth = Bezier!. The four line points $P_{1}$, \ldots{}, $P_{4}$ result in two quadratic splines and two straight line segments.}\label{fig:smooth-bezier}
\end{figure}
The \lstinline!smooth! attribute specifies that a line can be drawn as straight line
segments (\lstinline!None!) or using a spline (\lstinline!Bezier!), where the line's points
specify control points of a quadratic Bezier curve, see \cref{fig:smooth-bezier}.
For lines with only two points, the \lstinline!smooth! attribute has no effect.
For lines with three or more points ($P_{1}$, $P_{2}$, \ldots{}, $P_{n}$), the middle point of each line segment ($P_{12}$, $P_{23}$, \ldots{}, $P_{(n-1)n}$) becomes the starting point and ending
points of each quadratic Bezier curve. For each quadratic Bezier curve, the common point of the two line segment becomes the control point. For instance, point $P_{2}$ becomes the control point for
the Bezier curve starting at $P_{12}$ and ending at $P_{23}$. A straight line is drawn between the starting point of the line and the starting point of the first quadratic Bezier curve, as well as
between the ending point of the line and the ending point of the last quadratic Bezier curve.
In the illustration above, the square points ($P_{1}$, $P_{2}$, $P_{3}$, and $P_{4}$) represent the points that define the line, and the circle points ($P_{12}$, $P_{23}$, and $P_{34}$) are the
calculated middle points of each line segment. Points $P_{12}$, $P_{2}$, and $P_{23}$ define the first quadratic Bezier curve, and the points $P_{23}$, $P_{3}$, and $P_{34}$ define the second
quadratic Bezier curve. Finally a straight line is drawn between points $P_{1}$ and $P_{12}$ as well as between $P_{34}$ and $P_{4}$.
The values of the \lstinline!EllipseClosure! enumeration specify if and how the
endpoints of an elliptical arc are to be joined (see \cref{ellipse}).
\begin{lstlisting}[language=modelica]
type Arrow = enumeration(None, Open, Filled, Half);
type TextStyle = enumeration(Bold, Italic, UnderLine);
type TextAlignment = enumeration(Left, Center, Right);
\end{lstlisting}
Filled shapes have the following attributes for the border and interior.
\begin{lstlisting}[language=modelica]
record FilledShape "Style attributes for filled shapes"
Color lineColor = Black "Color of border line";
Color fillColor = Black "Interior fill color";
LinePattern pattern = LinePattern.Solid "Border line pattern";
FillPattern fillPattern = FillPattern.None "Interior fill pattern";
DrawingUnit lineThickness = 0.25 "Line thickness";
end FilledShape;
\end{lstlisting}
The extent/points of the filled shape describe the theoretical
zero-thickness filled shape, and the actual rendered border is then half
inside and half outside the extent.
\subsection{Component Instance}\label{component-instance}
A component instance can be placed within a diagram or icon layer. It
has an annotation with a \lstinline!Placement! modifier to describe the placement.
Placements are defined in term of coordinate systems transformations:
\begin{lstlisting}[language=modelica]
record Transformation
Point origin = {0, 0};
Extent extent;
Real rotation(quantity="angle", unit="deg")=0;
end Transformation;
\end{lstlisting}
The origin attribute defines the position of the component in the
coordinate system of the enclosing class. The \lstinline!extent! defines the
position, size and flipping of the component, relative to the \lstinline!origin!
attribute. The \lstinline!extent! is defined relative to the \lstinline!origin! attribute of the
component instance. Given an extent \{\{x1, y1\}, \{x2, y2\}\},
x2\textless{}x1 defines horizontal flipping and y2\textless{}y1 defines
vertical flipping around the center of the object.
The \lstinline!rotation! attribute specifies rotation of the extent around the point
defined by the \lstinline!origin! attribute.
The graphical operations are applied in the order: scaling, flipping and
rotation.
\begin{lstlisting}[language=modelica]
record Placement
Boolean visible = true;
Transformation transformation "Placement in the diagram layer";
Boolean iconVisible "Visible in icon layer; for public connector";
Transformation iconTransformation "Placement in the icon layer; for public connector";
end Placement;
\end{lstlisting}
If no \lstinline!iconTransformation! is given the \lstinline!transformation! is also used for
placement in the icon layer. If no \lstinline!iconVisible! is given for a public connector the
\lstinline!visible! is also used for visibility in the icon layer.
\begin{nonnormative}
A connector can be shown in both an icon layer and a diagram
layer of a class. Since the coordinate systems typically are different,
placement information needs to be given using two different coordinate
systems. More flexibility than just using scaling and translation is
needed since the abstraction views might need different visual placement
of the connectors. The attribute \lstinline!transformation! gives the placement in
the diagram layer and \lstinline!iconTransformation! gives the placement in the icon
layer. When a connector is shown in a diagram layer, its diagram layer
is shown to facilitate opening up a hierarchical connector to allow
connections to its internal subconnectors.
\end{nonnormative}
For connectors, the icon layer is used to represent a connector when it
is shown in the icon layer of the enclosing model. The diagram layer of
the connector is used to represent it when shown in the diagram layer of
the enclosing model. Protected connectors are only shown in the diagram
layer. Public connectors are shown in both the diagram layer and the
icon layer. Non-connector components are only shown in the diagram
layer.
\subsection{Extends clause}\label{extends-clause}
Each extends-clause (and short-class-definition, as stated in \cref{annotations-for-graphical-objects})
may have layer specific annotations which describe
the rendering of the base class' icon and diagram layers in the
subclass.
\begin{lstlisting}[language=modelica]
record IconMap
Extent extent = {{0, 0}, {0, 0}};
Boolean primitivesVisible = true;
end IconMap;
record DiagramMap
Extent extent = {{0, 0}, {0, 0}};
Boolean primitivesVisible = true;
end DiagramMap;
\end{lstlisting}
All graphical objects are by default inherited from a base class. If the
\lstinline!primitivesVisible! attribute is false, components and connections are
visible but graphical primitives are not.
\begin{itemize}
\item
If the extent of the extends-clause defines a null region (the
default), the base class contents is mapped to the same coordinates in
the derived class, and the coordinate system (including
preserveAspectRatio) can be inherited as described in
\cref{coordinate-systems}.
\item
If the extent of the extends-clause defines a non-null region, the
base class coordinate system is mapped to the region specified by the
attribute extent, if preserveAspectRatio is true for the base class
the mapping shall preserve the aspect ratio. The base class coordinate
system (and preserveAspectRatio) is not inherited.
\end{itemize}
\begin{example}
\begin{lstlisting}[language=modelica]
model A
extends B annotation(
IconMap(extent={{-100,-100}, {100,100}},primitivesVisible=false),
DiagramMap(extent={{-50,-50}, {0,0}},primitivesVisible=true)
);
end A;
model B
extends C annotation(DiagramMap(primitivesVisible=false));
...
end B;
\end{lstlisting}
In this example the diagram of \lstinline!A! contains the graphical primitives
from \lstinline!A! and \lstinline!B! (but not from \lstinline!C! since they were hidden in \lstinline!B!) -- the ones
from \lstinline!B! are rescaled, and the icon of \lstinline!A! contains the graphical primitives
from \lstinline!A! (but neither from \lstinline!B! nor from \lstinline!C!).
\end{example}
\subsection{Connections}\label{connections1}
A connection is specified with an annotation containing a \lstinline!Line! primitive
and optionally a Text-primitive, as specified below.
\begin{example}
\begin{lstlisting}[language=modelica]
connect(a.x, b.x)
annotation(Line(points={{-25,30}, {10,30}, {10, -20}, {40,-20}}));
\end{lstlisting}
\end{example}
The optional Text-primitive defines a text that will be written on the
connection line. It has the following definition (\emph{it is not equal
to the Text-primitive as part of graphics -- the differences are marked as bold lines}):
% NOTE: Technically just the names -- not the entire lines are marked in bold
\begin{lstlisting}[language=modelica]
record Text
extends GraphicItem;
extends FilledShape;
Extent extent;
String string;
Real fontSize = 0 "unit pt";
String fontName;
TextStyle textStyle[:];
Color textColor=lineColor;
TextAlignment horizontalAlignment = if index<0 then TextAlignment.Right else TextAligment.Left;
Integer index;
end Text;
\end{lstlisting}
The \lstinline!index! is one of the points of Line (numbered 1, 2, 3, \ldots{} where
negative numbers count from the end, thus -1 indicate the last one). The \lstinline!string!
may use the special
symbols \lstinline!"\%first"! and \lstinline!"\%second"! to indicate the connectors in the
connect-equation.
The \lstinline!extent! and \lstinline!rotation! are relative to the \lstinline!origin! (default \lstinline!{0,0}!)
and the \lstinline!origin! is relative to the point on the Line.
The textColor attribute defines the color of the text. The text is drawn
with transparent background and no border around the text (and without
outline). The contents inherited from FilledShape is deprecated, but kept for compatibility reasons.
The default value for \lstinline!horizontalAlignment! is deprecated.
Having a zero size for the extent is deprecated and is handled as if upper part is moved up an appropriate amount.
\begin{example}
\begin{lstlisting}[language=modelica]
connect(controlBus.axisControlBus1, axis1.axisControlBus) annotation (
Text(string="%first", index=-1, extent=[-6,3; -6,7]),
Line(points={{-80,-10},{-80,-14.5},{-79,-14.5},{-79,-17},{-65,-17},{-65,-65},{-25,-65}}));
\end{lstlisting}
Draws a connection line and adds the text \emph{axisControlBus1}
ending at \{-6, 3\}+\{-25, -65\} and 4 vertical units of space for the text.
Using a height of zero, such as \lstinline!extent=[-6,3; -6,3]! is deprecated, but gives similar result.
\end{example}
\subsection{Graphical primitives}\label{graphical-primitives}
This section describes the graphical primitives that can be used to
define the graphical objects in an annotation.
\subsubsection{Line}\label{line}
A line is specified as follows:
\begin{lstlisting}[language=modelica]
record Line
extends GraphicItem;
Point points[:];
Color color = Black;
LinePattern pattern = LinePattern.Solid;
DrawingUnit thickness = 0.25;
Arrow arrow[2] = {Arrow.None, Arrow.None} "{start arrow, end arrow}";
DrawingUnit arrowSize=3;
Smooth smooth = Smooth.None "Spline";
end Line;
\end{lstlisting}
Note that the \lstinline!Line! primitive is also used to specify the graphical
representation of a connection.
For arrows:
\begin{itemize}
\item
The arrow is drawn with an aspect ratio of 1/3 for each arrow half, i.e.,
if the arrow-head is 3~mm long an arrow with Half will extend 1~mm from the
mid-line and with Open or Filled extend 1~mm to each side, in total making the base 2~mm wide.
\item
The arrowSize gives the width of the arrow (including the imagined
other half for Half) so that lineThickness=10 and arrowSize=10 will
touch at the outer parts.
\item
All arrow variants overlap for overlapping lines.
\item
The lines for the Open and Half variants are drawn with lineThickness.
\end{itemize}
\subsubsection{Polygon}\label{polygon}
A polygon is specified as follows:
\begin{lstlisting}[language=modelica]
record Polygon
extends GraphicItem;
extends FilledShape;
Point points[:];
Smooth smooth = Smooth.None "Spline outline";
end Polygon;
\end{lstlisting}
The polygon is automatically closed, if the first and the last points
are not identical.
\subsubsection{Rectangle}\label{rectangle}
A rectangle is specified as follows:
\begin{lstlisting}[language=modelica]
record Rectangle
extends GraphicItem;
extends FilledShape;
BorderPattern borderPattern = BorderPattern.None;
Extent extent;
DrawingUnit radius = 0 "Corner radius";
end Rectangle;
\end{lstlisting}
The \lstinline!extent! attribute specifies the bounding box of the rectangle. If the
\lstinline!radius! attribute is specified, the rectangle is drawn with rounded
corners of the given radius.
\subsubsection{Ellipse}\label{ellipse}
An ellipse is specified as follows:
\begin{lstlisting}[language=modelica]
record Ellipse
extends GraphicItem;
extends FilledShape;
Extent extent;
Real startAngle(quantity="angle", unit="deg")=0;
Real endAngle(quantity="angle", unit="deg")=360;
EllipseClosure closure = if startAngle == 0 and endAngle == 360
then EllipseClosure.Chord
else EllipseClosure.Radial;
end Ellipse;
\end{lstlisting}
The \lstinline!extent! attribute specifies the bounding box of the ellipse.
Partial ellipses can be drawn using the \lstinline!startAngle! and \lstinline!endAngle!
attributes. These specify the endpoints of the arc prior to the stretch
and rotate operations. The arc is drawn counter-clockwise from
\lstinline!startAngle! to \lstinline!endAngle!, where startAngle and endAngle are defined
counter-clockwise from 3 o'clock (the positive x-axis).
The closure attribute specifies whether the endpoints specified by
\lstinline!startAngle! and \lstinline!endAngle! are to be joined by lines to the centre of the
extent (\lstinline!closure=EllipseClosure.Radial!), joined by a single straight line
between the end points (\lstinline!closure=EllipseClosure.Chord!), or left